On Wed, Feb 07, 2007 at 02:41:22PM -0600, Nick Apperson wrote:
> If it only did one playout you would be right, but imagine the following
> cases:
> case 1: White wins by .5 x 100, Black wins by .5 x 100
> case 2: White wins by 100.5 x 91, Black wins by .5 x 109
> the method that takes into account score would prefer the second case even
> though it has a lower winning percentage that may be represented by the fact
> that white is making an overplay for instance.  Obviously this is just one
> example, but there are many cases like this and overplays tend to be
> priveledged in a sense I would suspect with this kind of algorithm.

I have been thinking about this, and have to agree with you, averaging
the results gives pretty small numbers, that can easily be disturbed by
adding the winning scores to the mixture. 

But there is a way. If we do N play-outs, the effect of any single of
them is 1/N. If we make sure to scale the score to be less than half of
this, it can not disturb anything in cases where the number of wins is
different. Only in cases with exactly the same number of wins in the
play-outs, would the score break the tie.

In other words my "large" constant of 1000 was far too small. It would
have to be something like 2NM, where M is the maximum score (say 361).
Round it up to 1000N, and we should be safe.

I still believe it would make endgames look more reasonable, and
possibly even better, in case the winning program has overlooked a
detail somewhere, having a large margin of points on the board should
act as an insurance against small blunders. 

Or am still missing something obvious?

  - Heikki

Heikki Levanto   "In Murphy We Turst"     heikki (at) lsd (dot) dk

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